Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9751	22600^21499+21499^22600	97913	Hans Havermann	05/2020
9752	2^325215+12909	97900	Lelio R Paula	07/2016
9753	22619^21286+21286^22619	97898	Hans Havermann	04/2020
9754	(126852^19321-1)/(126852^139-1)	97892	Ryan Propper	11/2023
9755	(85*10^97876-49)/9	97877	Robert Price	12/2020
9756	7*10^97874-69	97875	Robert Price	01/2017
9757	5*10^97869-63	97870	Robert Price	04/2021
9758	(643*32^65022-23)/31	97870	Eric Chen	04/2023
9760	(17^79537+5^79537)/22	97865	Robert Price	06/2013
9759	15^83212+22	97865	Lelio R Paula	08/2016
9761	2^325087-109057	97861	Enzo Doria	04/2014
9762	2^325074+1870657	97858	Enzo Doria	05/2016
9764	2^325066-2111	97855	Yves Minet	08/2013
9763	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
9765	(8694^24841-1)/8693	97851	Serge Batalov	06/2022
9766	(21159^22621-1)/21158	97843	Serge Batalov	06/2022
9767	26660^4677+4677^26660	97842	Hans Havermann	12/2019
9768	18^77944-89	97841	Lelio R Paula	07/2016
9769	119^47136+118	97833	Norbert Schneider	09/2018
9770	6^125720-17663	97830	Enzo Doria	02/2013
9771	(73640^20101-1)/73639	97829	Serge Batalov	06/2022
9772	2^324972-2069	97827	Yves Minet	05/2013
9773	2^324958-4691	97823	Yves Minet	05/2019
9774	(8087^25033-1)/8086	97820	Serge Batalov	06/2022
9775	2^324944-2788319	97818	Enzo Doria	03/2016
9777	22845^19112+19112^22845	97807	Hans Havermann	10/2019
9776	(317^39107-1)/316	97807	Anonymous	04/2024
9778	(2^324898+1270)/2	97804	Stefano Morozzi	09/2020
9780	4*10^97799-9	97800	Erik Branger	11/2013
9779	2^324882+577294575	97800	Lelio R Paula	09/2016
9781	2^324863-1867921	97794	Enzo Doria	04/2016
9782	6^125662-18473	97785	Enzo Doria	03/2013
9783	12^90604+11	97779	Lelio R Paula	07/2016
9784	(29*10^97751+49)/3	97752	Robert Price	09/2021
9785	(37108^21391-1)/37107	97741	Serge Batalov	06/2022
9786	5^139830+24	97737	Lelio R Paula	04/2016
9787	(2^324672+1198)/2	97736	Stefano Morozzi	09/2020
9788	(101*10^97724+7)/9	97726	Robert Price	02/2022
9789	2^324612+1155	97718	Lelio R Paula	07/2016
9790	(2^324597+3542)/2	97714	Stefano Morozzi	09/2020
9791	19^76404-44	97702	Lelio R Paula	07/2016
9792	(5939^25889-1)/5938	97694	Serge Batalov	06/2022
9794	2^324505-2983	97686	Yves Minet	04/2011
9793	(7740^25121-1)/7739	97686	Serge Batalov	06/2022
9795	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
9796	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
9797	(11234^24109-1)/11233	97651	Serge Batalov	06/2022
9798	6^125488-17843	97649	Enzo Doria	02/2013
9799	(2^324350+3198)/2	97639	Stefano Morozzi	09/2020
9800	(75638^20011-1)/75637	97624	Serge Batalov	06/2022
9801	7^115515-2	97622	Lelio R Paula	09/2013
9802	(15672^23269-1)/15671	97613	Serge Batalov	06/2022
9803	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
9804	6^125418-5	97595	Lelio R Paula	11/2014
9805	(2^324193+3522)/2	97592	Stefano Morozzi	09/2020
9806	(2422^28837-1)/2421	97587	Serge Batalov	06/2022
9807	(2^324172+666)/2	97586	Stefano Morozzi	09/2020
9808	2^324091+111546435	97562	Paul Bourdelais	10/2021
9809	2^324076+1155	97557	Lelio R Paula	07/2016
9810	(2^324074+9)/13	97555	Lelio R Paula	10/2013
9811	(11*10^97539-71)/3	97540	Robert Price	04/2022
9812	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
9813	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
9814	2^323946+73939	97518	Enzo Doria	04/2016
9815	2^323937+1866947	97515	Enzo Doria	03/2016
9816	(98339^19531-1)/98338	97508	Serge Batalov	06/2022
9818	6^125290-18533	97495	Enzo Doria	03/2013
9817	(2^323870+1650)/2	97495	Stefano Morozzi	09/2020
9819	2^323845+101	97488	Lelio R Paula	12/2012
9820	18^77662+65	97487	Lelio R Paula	07/2016
9821	22634^20265+20265^22634	97479	Hans Havermann	04/2020
9822	(5533^26041-1)/5532	97467	Serge Batalov	06/2022
9823	2^323772+76771	97466	Enzo Doria	05/2016
9824	2^323765-112213	97463	Enzo Doria	06/2014
9825	22730^19389+19389^22730	97457	Hans Havermann	02/2020
9826	2^323720-6555	97450	Lelio R Paula	07/2016
9827	2^323694-1860401	97442	Enzo Doria	03/2016
9828	20^74886+3	97429	Lelio R Paula	06/2016
9829	24476^9561+9561^24476	97427	Hans Havermann	01/2020
9830	(2^323623+1766)/2	97420	Stefano Morozzi	09/2020
9831	(3250^27739-1)/3249	97413	Serge Batalov	06/2022
9833	3*10^97399+73	97400	Robert Price	04/2016
9832	7^115252-50	97400	Lelio R Paula	07/2016
9834	(4715^26513-1)/4714	97392	Serge Batalov	06/2022
9835	2^323521+213317	97390	Enzo Doria	09/2023
9836	224737#+393581	97389	Nicolas PALAU	12/2016
9837	(119374^19321-1)/(119374^139-1)	97386	Ryan Propper	11/2023
9838	(2^323468+3186)/2	97374	Stefano Morozzi	09/2020
9839	(2^323456+538)/2	97370	Stefano Morozzi	09/2020
9840	23277^15236+15236^23277	97365	Hans Havermann	07/2020
9842	(26*10^97353+31)/3	97354	Robert Price	07/2016
9841	(2^323403+3510)/2	97354	Stefano Morozzi	09/2020
9843	23756^12519+12519^23756	97342	Hans Havermann	07/2020
9844	10^97335+271641	97336	Patrick De Geest	09/2022
9846	10^97335-4000001	97335	Robert Price	07/2021
9845	10^97335-98193	97335	Patrick De Geest	09/2022
9847	(637*10^97331+11)/9	97333	Robert Price	10/2021
9848	23991^11402+11402^23991	97332	Hans Havermann	07/2020
9849	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
9850	(38*10^97329+187)/9	97330	Robert Price	11/2017
9851	(31147^21661-1)/31146	97328	Serge Batalov	06/2022
9852	86455!4+8	97319	Robert Price	09/2019
9853	22591^20310+20310^22591	97316	Hans Havermann	06/2020
9854	2^323261-431173	97312	Harrison Mesh	06/2022
9855	(3996^27017-1)/3995	97302	Serge Batalov	06/2022
9856	25101^7520+7520^25101	97297	Hans Havermann	05/2020
9857	(233*10^97294+7)/3	97296	Robert Price	03/2022
9858	p(19982)#/2-1024	97293	Robert Price	09/2017
9859	(65*10^97288+277)/9	97289	Robert Price	08/2021
9860	6^125021-85	97286	Lelio R Paula	08/2016
9861	2^323164-47355	97283	Lelio R Paula	07/2016
9862	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
9863	2^323054-6555	97249	Lelio R Paula	07/2016
9864	22822^18247+18247^22822	97249	Hans Havermann	02/2020
9865	9*10^97247-29	97248	Robert Price	05/2017
9866	24382^9735+9735^24382	97244	Hans Havermann	02/2020
9867	(31*10^97242+41)/9	97243	Robert Price	04/2015
9868	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
9869	12^90098-41	97233	Lelio R Paula	07/2016
9870	2^322928-216929	97212	Enzo Doria	05/2014
9871	(16731^23017-1)/16730	97209	Serge Batalov	06/2022
9872	3*10^97205-61	97206	Robert Price	04/2021
9873	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
9874	(35*10^97194-341)/9	97195	Robert Price	08/2021
9875	(4872^26357-1)/4871	97194	Serge Batalov	06/2022
9876	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
9877	(796*10^97183-31)/9	97185	Robert Price	07/2022
9878	(2^322789+2214)/2	97169	Stefano Morozzi	09/2020
9879	2^322725+75761	97150	Enzo Doria	04/2016
9880	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
9881	(2175^29101-1)/2174	97121	Serge Batalov	06/2022
9882	22402^21639+21639^22402	97118	Hans Havermann	07/2020
9883	23399^14128+14128^23399	97108	Hans Havermann	06/2020
9884	(2892^28057-1)/2891	97108	Serge Batalov	06/2022
9885	(9578^24391-1)/9577	97104	Serge Batalov	06/2022
9886	(2^322525+2606)/2	97090	Stefano Morozzi	09/2020
9887	(9563^24391-1)/9562	97087	Serge Batalov	06/2022
9888	(41*10^97085+373)/9	97086	Robert Price	04/2017
9889	(2^322473+854)/2	97074	Stefano Morozzi	02/2021
9890	2^322413+77	97056	Lelio R Paula	12/2012
9891	2^322406+177	97054	Lelio R Paula	12/2012
9892	(349^38167-1)/348	97050	Serge Batalov	06/2022
9893	(14*10^97044+31)/9	97045	Robert Price	02/2015
9894	2^322302+255255	97023	Lelio R Paula	07/2016
9895	2^322286+212659	97018	Enzo Doria	09/2023
9896	(1302^31147-1)/1301	97008	Serge Batalov	06/2022
9897	2^322196-113093	96991	Enzo Doria	07/2014
9898	(2^322169+2690)/2	96983	Stefano Morozzi	09/2020
9899	(49*10^96980+221)/9	96981	Robert Price	02/2022
9900	9*10^96968-47	96969	Robert Price	11/2021
9901	(5895^25717-1)/5894	96962	Serge Batalov	06/2022
9902	(27473^21841-1)/27472	96946	Serge Batalov	06/2022
9903	23109^15668+15668^23109	96943	Hans Havermann	07/2020
9904	2^322000-1861469	96932	Enzo Doria	03/2016
9905	2^321971-112747	96923	Enzo Doria	06/2014
9906	23754^12023+12023^23754	96917	Hans Havermann	07/2020
9907	11^93062-92	96915	Lelio R Paula	06/2016
9908	(37871^21169-1)/37870	96914	Serge Batalov	06/2022
9909	(2^321922+2214)/2	96908	Stefano Morozzi	09/2020
9910	(2^321900+2086)/2	96902	Stefano Morozzi	09/2020
9911	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
9912	3^203051+34	96880	Lelio R Paula	05/2016
9913	2*10^96867-51	96868	Robert Price	11/2017
9914	(2^321779+2618)/2	96865	Stefano Morozzi	09/2020
9915	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
9916	2^321716-2786939	96847	Enzo Doria	03/2016
9917	22496^20181+20181^22496	96844	Hans Havermann	03/2020
9918	2^321701-113053	96842	Enzo Doria	07/2014
9919	2^321700-28635	96842	Lelio R Paula	06/2016
9920	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
9921	6*10^96835+13	96836	Robert Price	10/2021
9922	6^124433-124433	96828	Robert Price	01/2014
9923	2^321631+69	96821	Lelio R Paula	12/2012
9924	(27109^21841-1)/27108	96820	Serge Batalov	06/2022
9925	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
9926	(5052^26141-1)/5051	96809	Serge Batalov	06/2022
9927	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
9928	(59*10^96798+31)/9	96799	Robert Price	09/2015
9929	(2^321536+2062)/2	96792	Stefano Morozzi	09/2020
9930	223319#+231223	96790	Makoto Morimoto	02/2016
9931	2^321519-28635	96787	Lelio R Paula	06/2016
9932	2^321487-1867237	96778	Enzo Doria	03/2016
9933	2^321461-63	96770	Lelio R Paula	12/2012
9934	(16053^23011-1)/16052	96770	Serge Batalov	06/2022
9935	2^321439+123	96763	Lelio R Paula	12/2012
9936	2^321434+709	96762	Lelio R Paula	02/2013
9937	2^321419+22703	96757	Enzo Doria	09/2023
9938	(2^321415+554)/2	96756	Stefano Morozzi	09/2020
9939	14^84413+89	96749	Lelio R Paula	07/2016
9940	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
9941	13^86847+96	96743	Lelio R Paula	06/2016
9942	9*2^321336-7	96733	Lelio R Paula	08/2014
9943	(209*10^96722-17)/3	96724	Robert Price	05/2017
9944	(54163^20431-1)/54162	96710	Serge Batalov	06/2022
9945	2^321237-4615	96702	Yves Minet	05/2019
9946	(27273^21799-1)/27272	96691	Serge Batalov	06/2022
9947	2^321187-1159	96687	Yves Minet	11/2012
9948	2^321182-1850081	96686	Enzo Doria	08/2015
9950	23359^13768+13768^23359	96680	Hans Havermann	06/2020
9949	(65630^20071-1)/65629	96680	Serge Batalov	06/2022
9951	2^321116-112829	96666	Enzo Doria	06/2014
9952	2^321108-109499	96664	Enzo Doria	04/2014
9953	2^321098+2793859	96661	Enzo Doria	03/2016
9954	(2^321100+1170)/2	96661	Stefano Morozzi	09/2020
9955	2^321057+4097	96648	Lelio R Paula	06/2016
9956	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
9957	22743^17750+17750^22743	96640	Hans Havermann	04/2020
9958	22882^16679+16679^22882	96612	Hans Havermann	02/2020
9959	23452^13163+13163^23452	96608	Hans Havermann	02/2020
9960	(1042^32009-1)/1041	96596	Serge Batalov	06/2022
9961	(85*10^96594-373)/9	96595	Robert Price	05/2021
9962	(2^320863+666)/2	96590	Stefano Morozzi	09/2020
9963	p(19849)#/2-64	96581	Robert Price	04/2017
9964	2^320817+189	96576	Lelio R Paula	12/2012
9965	2^320816-4685	96576	Yves Minet	05/2019
9967	(361*10^96567-163)/9	96569	Robert Price	10/2017
9966	(19*10^96568+137)/3	96569	Robert Price	03/2022
9968	2^320788-110327	96567	Enzo Doria	05/2014
9969	(3065^27697-1)/3064	96561	Serge Batalov	06/2022
9970	2^320764+793	96560	Lelio R Paula	02/2013
9971	(2^320752+1842)/2	96556	Stefano Morozzi	02/2021
9972	(48331^20611-1)/48330	96542	Serge Batalov	06/2022
9973	(107746^19321-1)/(107746^139-1)	96532	Ryan Propper	11/2023
9974	(50595^20521-1)/50594	96529	Serge Batalov	06/2022
9975	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
9976	23288^13947+13947^23288	96517	Hans Havermann	07/2020
9978	2^320616-78795	96516	Lelio R Paula	03/2016
9977	(19*10^96520+287)/9/109/409	96516	Alfred Reich	11/2022
9979	2^320612-461939	96514	Enzo Doria	07/2015
9980	(21245^22303-1)/21244	96507	Serge Batalov	06/2022
9981	10^96504+987654321	96505	Robert Price	12/2019
9982	10^96504+71887	96505	Patrick De Geest	02/2020
9983	22654^18195+18195^22654	96505	Hans Havermann	07/2020
9984	10^96504-139277	96504	Patrick De Geest	02/2020
9985	(218^41263-1)/217	96490	Serge Batalov	06/2022
9986	(47220^20641-1)/47219	96474	Serge Batalov	06/2022
9987	5*2^320431+7	96461	Lelio R Paula	08/2014
9988	19^75431-90	96458	Lelio R Paula	06/2016
9989	(11853^23677-1)/11852	96452	Serge Batalov	06/2022
9990	(2^320386+2814)/2	96446	Stefano Morozzi	02/2021
9991	(2^320370+3)/67	96440	Lelio R Paula	10/2013
9992	3*10^96431-17	96432	Robert Price	03/2021
9993	2^320309+1871477	96423	Enzo Doria	05/2016
9994	(10412^24001-1)/10411	96421	Serge Batalov	06/2022
9995	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
9996	(29*10^96407-23)/3	96408	Robert Price	03/2022
9997	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
9998	2^320232-173	96400	Lelio R Paula	12/2012
9999	175^42975-2	96395	Lelio R Paula	10/2017
10000	(2^320170+2718)/2	96381	Stefano Morozzi	09/2020

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Probable Primes Top 10000

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